No one ever makes a serious claim that Elaida's election is invalid. Even Siuan's closest supporters and Elaida's staunchest opponents such as Anaiya is characterized states that Elaida is the lawful Amyrlin. The very woman who nominated Siuan for the job agrees with the validity of Elaida's election, as well as the seniormost Sitter in the Hall, Saerin. Even the nuetral Cadsuane believes in Elaida's legitimacy. There is never a serious case against her advanced that is not propaganda or political spin. Even Egwene makes a backhanded nod to Elaida's legitimacy by having her Hall elect Egwene in her stead. You might say she was just be politic and allowing them to save face, but that doesn't fit with her words afterwards. Egwene is the Amyrlin because her side won the war by default. It had nothing to do with right or legitimacy, and any other view of the matter arises strictly from the PoV trap.